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Application of new robust design by means of probability-based multi-objective optimization to machining process parameters
Maosheng Zhenga, Haipeng Tengb, Yi Wangc
a Northwest University, School of Chemical Engineering, Xi'an, People's Republic of China, e-mail: [email protected], corresponding author, ORCID iD: https://orcid.org/0000-0003-3361-4060
b Northwest University, School of Chemical Engineering, Xi'an, People's Republic of China, e-mail: [email protected], ORCID iD: https://orcid.org/0000-0003-2987-7415
c Northwest University, School of Chemical Engineering, Xi'an, People's Republic of China, e-mail: [email protected], ORCID iD: https://orcid.org/0000-0001-6711-0026
DOI: 10.5937/vojtehg71 -39747; https://doi.org/10.5937/vojtehg71-39747
FIELD: materials, optimization ARTICLE TYPE: original scientific paper
Abstract:
Introduction/purpose: New robust design by means of probability-based multi-objective optimization takes the arithmetic mean value of the performance indicator and its deviation as twin independent responses of the performance indicator. The aim of this article is to check the applicability of new robust design in optimizing machining process parameters. To conduct the examination in detail, the robust design for optimal cutting parameters to minimize energy consumption during the turning of AIS11018 steel at a constant material removal rate is applied as well as the concurrent optimization of the machining process parameters and the tolerance allocation of a spheroidal graphite cast iron piston. Methods: In the spirit of the probability-based method for multi-objective optimization, the arithmetic mean value of the performance indicator and its deviation are taken as two independent responses of the performance indicator to implement robust design. Each of the above twin responses contributes one part of the partial preferable probabilities to the performance indicator of the alternatives in the treatment. The arithmetic mean value of the performance indicator should be assessed as a representative of the performance indicator according to the function or the preference of the performance indicator, and the deviation is the other
index of the performance indicator, which has the characteristic of the smaller-the-better in general. Furthermore, the square root of the product of the above two parts of the partial preferable probability forms the actual preferable probability of the performance indicator. Moreover, the product of partial preferable probabilities gives the total preferable probability of each alternative, which is the overall and unique index of each alternative in the robust optimum.
Results: The paper gives the rational optimum cutting parameters for minimizing energy consumption during the turning of AIS11018 steel at a constant material removal rate and the concurrent optimization of the machining process parameters and the tolerance allocation of a spheroidal graphite cast iron piston.
Conclusion: The application study indicates its rationality and convenience of new robust optimization in the optimization of machining process parameters.
Key words: preferable probability; probability-based method; multi-objective optimization; robust design; simultaneous optimization.
Introduction
The importance of quality improvement through reducing the effect of noise on response was recognized early in 1950s by Taguchi - Taguchi's method (Roy, 2010; Mori & Tsai, 2011). Designed experiments could be performed to study the effects of both controllable and uncontrollable factors on product or process response. Uncontrollable factors are called noise factors by Taguchi (Roy, 2010; Mori & Tsai, 2011). The idea of robust design corresponds to a design of a set of controllable factors which make the quality of a product insensitive to so-called noise factors or sensitive as little as possible i.e. with a minimum effect of noise (Roy, 2010; Mori & Tsai, 2011).
In Taguchi's method (Roy, 2010; Mori & Tsai, 2011), it was further assumed that controllable factors include factors that can be easily controlled by an experimenter or a product designer, such as design of a prescription or a melting temperature in an alloy melting process, while uncontrollable factors (noise factors) are those impossible or not easily possible to control. So, robust design is a concept seeking a set of controllable factors which make product and processes with minimum sensitivity to the variations of uncontrollable factors without removing uncontrollable factors.
Moreover, signal-to-noise ratio (SNR) was introduced by Taguchi as a specific term to characterize robust design (Roy, 2010; Mori & Tsai, 2011). Optimum factors correspond to a set of controllable factors which
guarantee an appropriate SNR maximum. There are three types of standard types of SNRs which were suggested by Taguchi: • Nominal-the-best
i —2 ^
y
SNRT = 10 log
V V
Smaller-the-better
( 1 2
SNRs = -10 log 7 X y Larger-the-better SNRl =-10 log
V2 i=i
and
^ 2 1 ^
1 X ^
2 i=1 y y
(1) (2)
(3)
In the above Eqs. (1) - (3), l stands for the number of each experimental test, y is the arithmetic mean value of the l data of
experimental tests, and a is the standard deviation.
The mean value y of the tests and the standard error a are inherently independent responses for a set of actual experiments or processes in general, which was pointed out by many statisticians - scientists (Box, 1988; Box & Meyer, 1986; Welch et al, 1990; Welch et al, 1992; Nair et al, 1992).
However, the SNR in Eq. (1) unites the two factors y and a into one factor SNRt unreasonably - the optimization of the maximum of the SNRt is not equivalent to the simultaneous optimizations of the both minima of a and y closing to the target. More problematically, the expressions of Eq. (2) and Eq. (3) for "smaller-the-better" and "larger-the-better" imply more serious cases, i.e., these formulae even exclude the factor of the standard deviation a. This point was frequently criticized by statisticians (Box, 1988; Box & Meyer, 1986; Welch et al, 1990; Welch et al, 1992; Nair et al, 1992). A kind advice from statisticians was to consider both responses of the mean and the variance by using two individual models.
Therefore, the optimization of the both minima of a and y closing to the target should be treated with two individual models at the same time so as to perform rational robust optimization.
In recent years, a probability-based method for multi-objective optimization (PMOO) was developed to solve the inherent problems of
2
the "additive algorithm" with personal and subjective factors in previous multi-objective optimizations (Zheng et al, 2022a; Zheng et al, 2022b; Zheng et al, 2023). A new concept of preferable probability was introduced to represent the preference degree of performance utility indicator of candidates in optimization. In this new methodology, all performance utility indicators of alternatives could be preliminarily divided into two types, i.e., beneficial or unbeneficial types according to their functions or pre-required preference in the optimization; every performance utility indicator of the alternative could quantitatively contribute to a partial preferable probability. Moreover, the product of all partial preferable probabilities leads to the total preferable probability of an alternative by means of the probability theory, which is the uniquely decisive index of a candidate in the optimization process, thus transfering a multi-objective optimization problem into a single-objective one.
This paper shows the application of new robust design by means of the probability theory with taking the arithmetic mean values of the performance indicators of the alternatives and their deviations as two independent factors rationally in order to deal with the problem of robust optimization of machining process parameters. Two examples - turning of AISI 1018 steel at a constant material removal rate and a concurrent optimization of the machining process parameters and the tolerance allocation of a spheroidal graphite cast iron piston - are given to show the rationality of robust design in manufacturing.
Rational process of robust design by means of probability-based multi-objective optimization
1) Fundamental principle of probability-based multi-objective optimization
In the methodology of the probability-based method for multi-objective optimization [8-10], a new concept of preferable probability was introduced to represent a preference degree of a performance utility indicator in optimization. All performance utility indicators of alternatives could be preliminarily divided into two types, i.e., beneficial or unbeneficial types according to their functions or pre-required preference in the optimization; every performance utility indicator of an alternative contributes to a partial preferable probability quantitatively; moreover, the product of all partial preferable probabilities leads to the total preferable probability of an alternative in the viewpoint of probability theory to reflect the essence of their simultaneous optimization, which is the unique
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decisive index in the optimization process, thus transfering a multi-objective optimization problem into a single-objective one (Zheng et al, 2022a; Zheng et al, 2022b; Zheng et al, 2023).
The formation of total preferable probability of an alternative by multiplying all partial preferable probabilities of their performance utility indicators reveals the spirit of simultaneous optimization of each performance utility indicator in the spirit of the probability theory explicitly, which undoubtedly solves the intrinsic problems of "additive algorithms" of subjective factors in previous multi-objective optimizations.
2) Process of new robust design by means of probability-based multi-objective optimization
In the light of the suggestion from statisticians that both responses of the mean and the variance could be taken into account by using two individual models, the process of rational robust design by means of probability-based multi-objective optimization is as follows.
A) The arithmetic mean value of the performance indicator of the alternatives and its deviation are taken as twin independent responses of the performance indicator to conduct robust design. Each of the above two responses contributes one part of the partial preferable probabilities to the performance indicator of the alternatives in the treatment of robust design.
B) The arithmetic mean value of the performance indicator should be assessed as a representative of the performance indicator according to its function and preference, and the deviation is the other index of the performance indicator which has the characteristic of the smaller-the-better in general.
C) The square root of the product of both parts of partial preferable probability of the performance indicator forms the actual preferable probability of the performance indicator.
D) The product of all partial preferable probabilities forms the total preferable probability of each alternative, which is the overall and unique index of each alternative in the robust optimum.
E) The total preferable probability of the alternatives is the unique index which is used as the decisive indicator of every alternative to complete the robust optimum.
Applications of robust design by means of probability-based multi-objective optimization
The application examples of new robust design by means of probability-based multi-objective optimization in robust design of products are given here to illustrate the new approach in detail.
1) Optimization of cutting parameters to minimize energy consumption during the turning of AIS11018 steel at a constant material removal rate
Camposeco-Negrete et al. conducted an optimization of cutting parameters to minimize energy consumption during the turning of AISI 1018 steel at a constant material removal rate. There are three control factors: the cutting speed (Factor A), the feed rate (Factor B), and the cut depth (Factor C) with three levels for each factor, as shown in Table 1 by means of the Taguchi Lg(34) design with four test results (Camposeco-Negrete et al, 2016). The aim of this experimental design is to apply robust design for the optimization of energy consumption. The values of the cutting parameters shown in Table 1 were calculated in order to obtain a constant material removal rate of 1333.33 mm3/s (Camposeco-Negrete et al, 2016).
Table 1 - Values and levels of the cutting parameters of AIS11018 steel at a constant material removal rate by means of L9(34) Таблица 1 - Значения и уровни параметров резки стали AIS11018 при постоянной скорости съема материала с помощью Lg(34)
Табела 1 - Вредности и нивои параметара сечена челика АИСИ 1018 при константно] брзини уклаъаъа материала помоПу Lg(34)
Exp. no Factor values Energy consumed (kJ)
A (m/min) B (mm/rev) C (mm) 1 2 3 4
1 350 0.10 2.29 71.47 74.2 121.04 133.14
2 350 0.15 1.52 51.64 54.28 88.85 97.22
3 350 0.20 1.14 42.93 43.63 73.07 80.75
4 375 0.10 2.13 68.97 71.10 123.99 135.69
5 375 0.15 1.42 51.67 52.49 91.19 100.17
6 375 0.20 1.07 42.00 43.04 76.29 82.66
7 400 0.10 2.00 67.94 69.47 130.63 141.77
8 400 0.15 1.33 50.41 52.17 97.35 105.91
9 400 0.20 1.00 41.08 42.05 81.44 86.75
Table 2 shows the assessed results of the preferable probability and the ranks of this problem.
The mean value of energy consumption is shown by у, and the standard deviation is represented by s.
According to the requirement of robust optimization, the performances of у and s have the characteristic of the unbeneficial indexes in Table 2.
Table 2 - Assessed results of the preferable probability and the rank of AIS11018 steel at a constant material removal rate by means of L9(34)
Таблица 2 - Результаты оценки предпочтительной вероятности и ранга стали AIS11018 при постоянной скорости съема материала с помощью L9(34)
Табела 2 - Анализирани резултати поже^не вероватноПе и ранга челика АИСИ 1018 при константно] брзини уклаъаъа материала помоПу L9(34)
Exp. no Mean value of energy consumption p (kJ) S. D. of energy consumption s (kJ) Preferable probability
Pp Ps Pt=(Pp-Ps) 05 Rank
1 99.9625 31.7308 0.0831 0.0946 0.0887 7
2 72.9975 23.4131 0.1189 0.1291 0.1239 4
3 60.0950 19.6699 0.1360 0.1447 0.1403 1
4 99.9375 34.8681 0.0831 0.0816 0.0823 8
5 73.8800 25.4402 0.1177 0.1207 0.1192 5
6 60.9975 21.4981 0.1348 0.1371 0.1359 2
7 102.4525 39.2377 0.0798 0.0635 0.0712 9
8 76.4600 29.2820 0.1143 0.1048 0.1094 6
9 62.8300 24.6534 0.1324 0.1240 0.1281 3
The assessed results in Table 2 indicate that test No. 3 has the highest value of the total preferable probability Pt at the first glance. Therefore, the robust configuration is around tests No. 3.
Moreover, Table 3 shows the results of the range analysis for the total preferable probability shown in Table 2, which shows that the optimum configuration is A1B3C1, which is test No. 3 exactly.
C^D
Table 3 - Range analysis of the total preferable probability of AIS11018 steel at a constant material removal rate by means of L9(34)
Таблица 3 - Анализ ранжирования общей предпочтительной вероятности стали AIS11018 при постоянной скорости съема материала с помощью Lg(34)
Табела 3 - Анализа рангираша укупне поже^не вероватноПе челика АИСИ 1018 при константно] брзини уклаъаъа материала помоПу Lg(34)
Level A B C
1 0.1176 0.0807 0.1348
2 0.1125 0.1175 0.1175
3 0.1029 0.1348 0.0807
Range 0.0147 0.0540 0.0540
Order 3 1 2
Optimal configuration A1 B3 C1
2) Concurrent optimization of the machining process parameters and the tolerance allocation of a spheroidal graphite cast iron piston
Janakiraman & Saravanan conducted a concurrent optimization of the machining process parameters and the tolerance allocation of a spheroidal graphite cast iron piston (2010) as an example of conducting a restudy with robust design of probability-based multi-objective optimization.
There are 3 control factors: cutting speed (A), feed rate (B), and depth of cut (C) with five levels in the experiments with response surface methodology design and the test results, as shown in Table 4.
The mean value of energy consumption is shown by y, and the standard deviation is represented by s. As the target value is the input diameter (Janakiraman & Saravanan, 2010), a factor s is introduced to present the deviation of the mean value from the target value of the input diameter, i.e., s= - input diameter |.
Furthermore, according to the requirement of robust design, the performance of s and s has the characteristic of unbeneficial indexes. All the assessed results are shown in Table 5 together with their preferable probability values and ranks.
dD
Table 4 - Response surface central composite rotatable design matrix and the test
results
Таблица 4 - Поверхность отклика матрицы центральной композитной вращающейся конструкции и результаты испытаний
Табела 4 - Површина одговора матрице централног композитног ротационог дизайна и резултати испитиваъа
Expt. no. Cutting speed (A) (m/min) Feed rate (B) (mm/rev) Depth of cut (C) (mm)
1 24.05 2.01 0.014
2 35.95 2.05 0.014
3 24.05 4.99 0.014
4 35.95 4.99 0.014
5 24.05 2.01 0.041
6 35.95 2.01 0.041
7 24.05 4.99 0.041
8 35.95 4.99 0.041
9 20 3.5 0.028
10 40 3.5 0.028
11 30 1 0.028
12 30 6 0.028
13 30 3.5 0.005
14 30 3.5 0.05
15 30 3.5 0.028
16 30 3.5 0.028
17 30 3.5 0.028
18 30 3.5 0.028
19 30 3.5 0.028
20 30 3.5 0.028
с®
Continued
Expt. no. Input diameter (mm) Output diameter measured (mm)
1 2 3 4 5
1 51.003 50.992 50.986 50.99 50.993 50.982
2 51.24 51.222 51.221 51.224 51.225 51.225
3 51.24 51.221 51.221 51.222 51.221 51.22
4 51.237 51.21 51.219 51.211 51.215 51.218
5 51.22 51.17 51.175 51.18 51.173 51.171
6 51.17 51.129 51.13 51.129 51.128 51.13
7 51.235 51.198 51.199 51.195 51.196 51.2
8 51.1 51.059 51.066 51.05 51.056 51.054
9 51.23 51.205 51.2 51.205 51.203 51.202
10 51.2 51.176 51.172 51.174 51.171 51.172
11 51.245 51.205 51.21 51.208 51.205 51.203
12 51.215 51.181 51.188 51.186 51.187 51.179
13 51.245 51.244 51.24 51.245 51.240 51.242
14 51.22 51.18 51.185 51.178 51.18 51.18
15 51.235 51.21 51.215 51.21 51.212 51.218
16 51.24 51.212 51.22 51.219 51.218 51.215
17 51.21 51.17 51.168 51.165 51.164 51.162
18 51.23 51.19 51.195 51.185 51.188 51.19
19 51.17 51.135 51.141 51.141 51.142 51.136
20 51.21 51.185 51.18 51.18 51.182 51.173
The assessed results in Table 5 indicate that test No. 13 has the highest value of the total preferable probability Pt that is closely followed by test No. 3.
Therefore, the robust configuration is around tests No. 13, while test No. 13 clearly shows simultaneous smaller values of both s and s from Table 5.
Table 5 - Assessed results together with the preferable probabilities and ranks Таблица 5 - Результаты анализа с предпочтительными вероятностями и
ранжированием
Табела 5 - Анализирани резултати са поже^ним вероватно-Ьама и рангираъем
Expt. no. И s s Preferable probability Rank
Ps Ps Pt=(PrPs) 05
1 50.9886 0.0144 0.0046 0.0750 0.0293 0.0469 12
2 51.2234 0.0166 0.0018 0.0715 0.0668 0.0691 3
3 51.2210 0.019 0.0007 0.0676 0.0820 0.0744 2
4 51.2146 0.0224 0.0040 0.0621 0.0365 0.0476 11
5 51.1738 0.0462 0.0040 0.0234 0.0375 0.0296 19
6 51.1292 0.0408 0.0008 0.0322 0.0802 0.0508 8
7 51.1976 0.0374 0.0021 0.0377 0.0633 0.0489 9
8 51.0570 0.0430 0.0060 0.0286 0.0097 0.0166 20
9 51.2030 0.0270 0.0021 0.0546 0.0627 0.0585 5
10 51.1730 0.0270 0.0020 0.0546 0.0643 0.0593 4
11 51.2062 0.0388 0.0028 0.0354 0.0537 0.0436 14
12 51.1842 0.0308 0.0040 0.0484 0.0375 0.0426 15
13 51.2422 0.0028 0.0023 0.0939 0.0605 0.0754 1
14 51.1806 0.0394 0.0026 0.0344 0.0560 0.0439 13
15 51.2130 0.0220 0.0035 0.0627 0.0443 0.0527 7
16 51.2168 0.0232 0.0033 0.0608 0.0470 0.0534 6
17 51.1658 0.0442 0.0032 0.0266 0.0480 0.0358 18
18 51.1896 0.0404 0.0036 0.0328 0.0418 0.0370 17
19 51.1390 0.0310 0.0032 0.0481 0.0474 0.0477 10
20 51.1800 0.0300 0.0044 0.0497 0.0313 0.0395 16
Conclusion
The above discussion indicates that new robust design by means of probability-based multi-objective optimization can be reasonably used to deal with the problem of optimizing machining process parameters. The arithmetic mean value of the performance indicator and its deviation are taken as twin independent responses of the performance indicator in the treatment, which contributes their parts of partial preferable probability of the performance indicator respectively. The arithmetic mean value of the
performance indicator is assessed as a representative of the performance indicator according to its function and preference, and the deviation is the unbeneficial index in the assessment. The total preferable probability of each alternative is the uniquely overall index of each alternative in the robust optimum.
References
Box, G. 1988. Signal-to-Noise Ratios, Performance Criteria, and Transformations. Technometrics, 30(1), pp.1-17. Available at: https://doi.org/10.2307/1270311.
Box, G.E.P. & Meyer, R.D. 1986. Dispersion Effects from Fractional Designs. Technometrics, 28(1), pp.19-27. Available at: https://doi.org/10.1080/00401706.1986.10488094.
Camposeco-Negrete, C., de Dios Calderón Nájera, J. & Miranda-Valenzuela, J.C. 2016 Optimization of cutting parameters to minimize energy consumption during turning of AISI 1018 steel at constant material removal rate using robust design. The International Journal of Advanced Manufacturing Technology, 83, pp.1341-1347. Available at: https://doi.org/10.1007/s00170-015-7679-9.
Janakiraman, V. & Saravanan, R. 2010. Concurrent optimization of machining process parameters and tolerance allocation. The International Journal of Advanced Manufacturing Technology, 51, pp.357-369. Available at: https://doi.org/10.1007/s00170-010-2602-x.
Mori, T. & Tsai, S-C. 2011. Taguchi Methods: Benefits, Impacts, Mathematics, Statistics, and Applications. New York, NY, USA: ASME Press. Available at: https://doi.org/10.1115Z1.859698.
Nair, V.N., Abraham, B., MacKay, J., Box, G., Kacker, R.N., Lorenzen, T.J., Lucas, J.M., Myers, R.H., Vining, G.G., Nelder, J.A., Phadke, M.S., Sacks, J., Welch, W.J., Shoemaker, A.C., Tsui, K.L., Taguchi, S. & Wu, C.F.J. 1992. Taguchi's Parameter Design: A Panel Discussion. Technometrics, 34(2), pp.127161. Available at: https://doi.org/10.2307/1269231.
Roy, R.K. 2010. A Primer on the Taguchi Method. 2nd Ed. Southfield, Michigan, USA: Society of Manufacturing Engineers. ISBN-13: 978-0872638648.
Welch, W.J., Buck, R.J., Sacks, J., Wynn, H.P., Mitchell, T.J. & Morris, M.D. 1992. Screening, Predicting, and Computer Experiments. Technometrics, 34(1), pp.15-25. Available at: https://doi.org/10.2307/1269548.
Welch, W.J., Yu, T-K., Kang, S.M. & Sacks, J. 1990. Computer experiments for quality control by parameter design. Journal of Quality Technology, 22(1), pp.15-22. Available at:
https://doi.org/10.1080/00224065.1990.11979201.
Zheng, M., Teng, H., Yu, J., Cui ,Y. & Wang Y. 2023. Probability-Based Multi-objective Optimization for Material Selection. Singapore: Springer. Available at: https://doi.org/10.1007/978-981-19-3351-6.
Zheng, M., Wang, Y. & Teng, H. 2022a. An novel method based on probability theory for simultaneous optimization of multi - object orthogonal test design in material engineering. Kovove Materialy, 60(1), pp.45-53. Available at: https://doi.org/10.31577/km.2022.1.45.
Zheng, M., Wang, Y. & Teng, H. 2022b. A novel approach based on probability theory for material selection. Materialwissenschaft und Werkstofftechnik, 53(6), pp.666-674. Available at:
https://doi.org/10.1002/mawe.202100226.
Многокритериальная оптимизация, основанная на вероятности в качестве основы для применения новой робастной конструкции с параметрами механической обработки
Маошенг Чжэн, корреспондент, Хайпэн Te^ Йи Вон Северо-западный политехнический университет, факультет химической инженерии, г. Сиань, Народная Республика Китай
РУБРИКА ГРНТИ: 27.47.00 Математическая кибернетика, 27.47.19 Исследование операций, 81.09.00 Материаловедение ВИД СТАТЬИ: оригинальная научная статья
Резюме:
Введение/цель: Новая робастная конструкция, разработанная с помощью многокритериальной оптимизации, основанной на вероятности, использует среднее арифметическое значение показателя эффективности и его отклонение как две независимые реакции показателей эффективности. Цель этой статьи - проверить применимость новой робастной конструкции для оптимизации параметров при механической обработке. При детальных испытаниях была использована робастная конструкция для определения оптимальных параметров резки и минимизации энергопотребления при токарной обработке стали AISI 1018, с учетом постоянной скорости съема материала, а также одновременной оптимизации параметров обработки и распределения допусков поршня из чугуна с шаровидным графитом. Методы: Придерживаясь метода, основанного на вероятности многокритериальной оптимизации, среднее арифметическое значение показателя эффективности и его отклонений используются в качестве двух независимых откликов показателя эффективности для ввода в эксплуатацию робастной конструкции. Каждый из вышеописанных двойных откликов частичными предпочтительными вероятностями способствует улучшению показателей эффективности
альтернатив в процессе испытаний. Среднее арифметическое значение показателя эффективности следует оценивать, как репрезентативное значение показателя эффективности в соответствии с функцией или преимуществом показателя эффективности, а отклонение является вторым показателем индикатора эффективности, который в целом характеризуется как «меньше-лучше». Кроме того, квадратный корень произведения двух вышеуказанных частей частичной предпочтительной вероятности формирует фактическую предпочтительную вероятность показателя эффективности. Более того, произведение частичных предпочтительных вероятностей дает общую предпочтительную вероятность по каждой альтернативе, которая является общим и уникальным индексом каждой из альтернатив в робастном оптимуме.
Результаты: В статье приведены рациональные оптимальные параметры резки для минимизации энергопотребления во время токарной обработки стали 1018 при постоянном съеме материала, а также одновременной оптимизации параметров обработки и распределения допусков поршня из чугуна с шаровидным графитом.
Выводы: Исследование показало, что применение новой робастной оптимизации является рациональным и удобным способом оптимизации параметров механической обработки.
Ключевые слова: предпочтительная вероятность; вероятностный метод; многокритериальная оптимизация; робастная конструкция; одновременная оптимизация.
Вишекритери]умска оптимизаци]а заснована на вероватнойи као основа за примену новог робустног диза]на на параметре машинске обраде
Маошенг Ценг, аутор за преписку, Хаипенг Тенг, Jи Ванг Универзитет Северозапад, Факултет хеми]ског инженерства, Си]ан, Народна Република Кина
ОБЛАСТ: математика, матери]али
КАТЕГОРША (ТИП) ЧЛАНКА: оригинални научни рад
Сажетак:
Увод/цил>: Нови робустни диза}н настао помогу вишекритери]умске оптимизаци]е засноване на вероватноЬи узима аритметичку средъу вредност индикатора перформанси, као и ььену деви}аци}у, за дво}не независне одговоре индикатора
перформанси. Цил овог рада ¡есте да се провери применливост новог робустног дизана на оптимизаци]у параметара машинске обраде. За детално испитиваше коришЬен ]е робустни диза]н за одре^иваше оптималних параметара сечена како би се потрошша енерги]е током окреташа челика АИСИ 1018, при константно/' брзини уклашаша материала, свела на на]машу могуЬу меру. Поред тога, истовремено ]е примешена и оптимизаци]а параметара машинске обраде и алокаци]а толеранци]е клипа од сфероидног графитног ливеног гвож^а.
Методе: У складу с методом заснованом на вероватноЬи за вишекритери]умску оптимизаци]у, аритметичка средша вредност индикатора перформанси. као и шена деви]аци]а, узете су за дво]не независне одговоре индикатора перформанси при примени робустног диза]на. Сваки од ова два поменута одговора доприноси ]едним делом парци]алних пожелних вероватноЬа индикатору перформанси алтернатива у испитивашу. Аритметичка средша вредност индикатора перформанси треба да се процешу]е као представник индикатора перформанси према функции или преференции индикатора перформанси, док ]е деви]аци]а други шихов показател кога, уопштено говореЬи, каракактерише принцип „маше ]е боле". Поред тога, квадратни корен производа два поменута дела парци]алне пожелне вероватноЬе формира стварну пожелну вероватноЬу индикатора перформанси. Штавише, производ парци]алних пожелних вероватноЬа да]е укупну пожелну вероватноЬу сваке алтернативе, што представла укупни и ]единствени индекс сваке алтернативе у робустном оптимуму.
Резултати: У раду су представлени рационални оптимални параметри сечеша за минимизираше потрошше енерги]е током окреташа челика АИСИ 1018 при константно] брзини уклашаша материала, као и истовремена оптимизаци]а параметара машинске обраде и алокаци]а толеранци]е клипа од сфероидног графитног ливеног гвож^а.
Заклучак: Студи]а указу]е да ]е примена нове робустне оптимизаций рационална и погодна за оптимизаци]у параметара машинске обраде.
Клучне речи: пожелна вероватноЬа, метод заснован на вероватноЬи, вишекритери]умска оптимизаци]а, робустни дизан, истовремена оптимизаци]а.
Paper received on / Дата получения работы / Датум приема чланка: 22.08.2022. Manuscript corrections submitted on / Дата получения исправленной версии работы / Датум достав^ана исправки рукописа: 26.01.2023.
Paper accepted for publishing on / Дата окончательного согласования работы / Датум коначног прихватана чланка за об]ав^иване: 28.01.2023.
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